Defining parameters
Level: | \( N \) | = | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | = | \( 8 \) |
Nonzero newspaces: | \( 1 \) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(16\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(6))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 9 | 1 | 8 |
Cusp forms | 5 | 1 | 4 |
Eisenstein series | 4 | 0 | 4 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)
We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
6.8.a | \(\chi_{6}(1, \cdot)\) | 6.8.a.a | 1 | 1 |
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(6))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_1(6)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 1}\)